Step-by-step explanation: *First, decide which volume formula to use: v = lwh
*Next, substitute in for what you do know (leave variable for unknown): 288 = 12 · w · 6
*Then simplify the side of the equation with the variable: 288 = 72 · w
*Now divide each side of the equation by 72 to solve for w:
288 ÷ 72 = w
4 in = w
compute the divergence ∇ · f and the curl ∇ ✕ f of the vector field. (your instructors prefer angle bracket notation < > for vectors.) f = 2x2, −3y2, z2
For the vector field f = 2x², −3y², z², Divergence (∇·f) = 4x - 6y² + 2z, Curl (∇×f) = (0, 0, 0).
To compute the divergence (∇·f) and the curl (∇×f) of the vector field f = (2x², -3y², z²), we can use the vector calculus operators. Divergence (∇·f),
In this case, the divergence of f is the partial derivative of each part of the field, for f = (2x², -3y², z²), we have,
∂f₁/∂x = 4x
∂f₂/∂y = ∂(-3y²)/∂y = -6y²
∂f₃/∂z = 2z
Therefore, the divergence of f is,
∇·f = 4x - 6y² + 2z
Curl (∇×f),
The curl of a vector field f = (f₁, f₂, f₃) is given by the cross product of the curl operator (∇×) and the vector field. In this case, the curl of f is,
∇×f = (i∂/∂x + j∂/∂y + k∂/∂y) x (i2x², -j3y², kz²)
Basically we can write (i2x², -j3y², kz²) as (f₁, f₂, f₃)
we have,
∂f₁/∂z = 0
∂f₂/∂x = ∂(-3y²)/∂x = 0
∂f₃/∂y = ∂(z²)/∂y = 0
Therefore, the curl of f is,
∇×f = (0, 0, 0)
In this case, the curl of f is the zero vector, indicating that the vector field f is irrotational.
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Complete question - compute the divergence ∇·f and the curl∇✕f of the vector field. f = 2x², −3y², z².
When a<0 is the parabols wider or narrower?
Answer:
When A is less than 0 the parabola flips downward. When A becomes larger than 1, the parabola becomes more narrow. When A becomes smaller, until 0, the parabola widens.
Step-by-step explanation:
EXERCISE 3: Find the limit or prove it fails to exist: a/ ž tz lim 2+4+3i Re(z - i) b/ lim zi zi = EXERCISE 4: Let f(x) = x3 + iy (i) Where has f the derivative? (ii) Where is f analytic?
a/ To find the limit of the expression 2 + 4 + 3i Re(z - i), we need to replace z with the limit point. Therefore, the expression will be:2 + 4 + 3i Re(z - i) = 6 + 3i Re(z - i)
We have to find the limit as z approaches i. Consider the following:
Since Re(z - i) is a real number, the limit can be found by setting Re(z - i) = 0.
Therefore, lim 2+4+3i Re(z - i) = lim 6 + 3i Re(z - i) = 6.Explanation:
b/ Given the limit lim zi / zi, we can simplify the expression by canceling zi in the numerator and the denominator. Therefore, lim zi / zi = lim 1 = 1.
Explanation:
4. Let f(x) = x3 + iy(a) The derivative of f(x) is the function f′(x). To find the derivative of f(x), we need to differentiate the real and imaginary components of f(x) separately.
Therefore, f′(x) = 3x² + iy, since the derivative of i is zero.
Explanation: (b) We must test the Cauchy-Riemann equations to see if f(x) is analytic. f(x) is said to be analytic if it meets the Cauchy-Riemann conditions. Therefore, we need to verify that the following equations are satisfied: ∂u / ∂x = ∂v / ∂y and ∂u / ∂y = -∂v / ∂x. Using the function given above, we can easily obtain its real and imaginary components. u(x, y) = x³ and v(x, y) = y. Therefore, ∂u / ∂x = 3x² and ∂v / ∂y = 1, but 3x² ≠ 1
Therefore, the Cauchy-Riemann equations are not satisfied, so f(x) is not analytic.
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At a particular university, students' grades in introductory statistic classes are generally unimodal and skewed to the left with a mean of μ = 68 and a standard deviation of σ = 17.2. (Round your answers to four decimal places, if needed.)
(a) The distribution of students' grades is is approximately normal is exactly normal may or may not be normal is left-skewed is right-skewed.
(b) If n = 30 students are selected at random, the distribution of the sample mean grade is approximately normal not normal left-skewed right-skewed with a mean of ? and a standard deviation of .
(c) The probability that the sample mean grade for these 30 students is less than 72.0 is .
(d) If n = 30 students are selected at random, the distribution of the sample total grade is approximately normal not normal left-skewed right-skewed with a mean of ? and a standard deviation of .
(e) The probability that the total grade for these 30 students is less than 2160.0 is .
The answers are =
a) left-skewed
b) Standard Error ≈ 3.146
c) the probability is approximately 0.7867.
d) standard deviation of = 94.094.
e) the probability is approximately 0.8669.
(a) The distribution of students' grades is left-skewed.
(b) If n = 30 students are selected at random, the distribution of the sample mean grade is approximately normal with a mean of 68 and a standard deviation of 3.146.
To calculate the standard deviation of the sample mean, also known as the standard error, you divide the population standard deviation by the square root of the sample size:
Standard Error = σ / √n = 17.2 / √30 ≈ 3.146
(c) To find the probability that the sample mean grade for these 30 students is less than 72.0, we can use the z-score formula and the standard error calculated above:
z = (x - μ) / (σ / √n)
z = (72 - 68) / (17.2 / √30) ≈ 0.7952
Now, we can use a standard normal distribution table or a calculator to find the probability corresponding to this z-score.
From the table or calculator, the probability is approximately 0.7867.
(d) If n = 30 students are selected at random, the distribution of the sample total grade is approximately normal with a mean of 30 × 68 = 2040 and a standard deviation of √(30) × 17.2 = 94.094.
The mean of the sample total grade is the product of the population mean and the sample size (n).
The standard deviation of the sample total grade is the product of the population standard deviation and the square root of the sample size (n).
(e) To find the probability that the total grade for these 30 students is less than 2160.0, we can use the z-score formula and the standard deviation calculated above:
z = (x - μ) / (σ × √n)
z = (2160 - 2040) / (17.2 × √30) ≈ 1.105
Using the standard normal distribution table or a calculator, the probability corresponding to this z-score is approximately 0.8669.
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PLEASE HELP ME SOMEONE. How do I do this? Please explain and I will give you crown.
Answer: the one in the bottom right
Step-by-step explanation: each month which is the x axis ( the bottom line) the y axis (line on the left) goes up by 5
so when the x axis is 1 the y axis should be at 5
Question
Find the volume of the cylinder. Find the volume
of a cylinder with the same radius and double the
height
7 in
3 in
Answer:
I couldn't really see the height number (that had to doubled) ir really the radius but I saw 7 for the radius and 3 (×2) for the height so I did the math and the answer is 923.63
Step-by-step explanation:
i could be wrong tho, hope this helped
Answer:
923.63
Step-by-step explanation: hope this helps!!
PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!
5cm
Step-by-step explanation:
volume of cube= l³
125 =l³
3root over 125 =l
l = 5
Answer:
So the length of the edge of a cube with a volume of 125 is 5.
Step-by-step explanation:
If the estimate being tested is less than the benchmark, you should conduct a ______ one-sample hypothesis test.
a. two tail
b. right tail
c. left tail
d. no tail
e. All of the choices above
f. None of the choices
If the estimate being tested is less than the benchmark, you should conduct a left tail one-sample hypothesis test. So, correct option is C.
In hypothesis testing, the null hypothesis typically assumes that there is no significant difference or effect, and the alternative hypothesis proposes that there is a significant difference or effect.
In this case, since the estimate is less than the benchmark, the alternative hypothesis would state that there is a significant difference, and we are specifically interested in detecting a decrease or a lower value.
Therefore, we conduct a left tail test to evaluate the evidence against the null hypothesis and determine if the estimate is significantly lower than the benchmark.
A left tail test focuses on the leftmost portion of the distribution and calculates the probability of observing a value as extreme or more extreme than the estimate, assuming the null hypothesis is true.
By comparing the test statistic with the critical value or p-value associated with the chosen significance level, we can make conclusions about the statistical significance of the estimate being less than the benchmark.
So, correct option is C.
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Find the measure of each number:
Step-by-step explanation:
11. angles 1 and 2 are vertical angles, meaning they are congruent.
angle 2=angle 1=38 degrees
14. angles 1 and 2 are supplementary angles, meaning they add to 180 degrees.
angle 1=180-angle 2=180-67=113 degrees
There are 6 friends baking bread. They equally share 3 sticks of butter. Write an equation to find the fraction of a stick of butter that each friend uses. 3 sticks of butter Choose the correct answer below. A. 3÷6= 6 3 B. 3÷6= 3 6 C. 6÷3= 3 6 D. 6÷3= 6 3
Answer:
B.
Step-by-step explanation:
the three sticks of butter were divided among six people
Right answer will be marked brainlist .
Answer:
$1159.69
Step-by-step explanation:
A = P (1 + r/n)^nt
A = 1000 (1 + 0.05/2)^2(3)
A = $1159.69
identify the graph that represents the given system of inequalities. also, identify two ordered pairs that are solutions to the system. y ≤ x 5 y ≤ 2x 3
Ordered pair (0, 6) and (2, 7) satisfy both inequalities in the system and are solutions to the system.
To identify the graph that represents the given system of inequalities y > x + 5 and y ≥ 2x + 3, we need to graph the individual inequalities and find the region where they overlap.
When we plot the graph of inequality separately:
y > x + 5:Draw a dashed line y = x + 5 (not including the line).Shade the region above the line.2. y ≥ 2x + 3:
Draw a solid line y = 2x + 3 (including the line).Shade the region above the line.The overlapping shaded region represents the solution to the system of inequalities.
To find two ordered pairs that are solutions to the system, we can choose any points within the overlapping region. Let's select two points:
Ordered pair 1: (0, 6)
Ordered pair 2: (2, 7)
These two points satisfy both inequalities in the system and are solutions to the system.
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The correct question is given below -
Identify the graph that represents the given system of inequalities. Also identify two ordered pairs that are solutions to the system.
y > x + 5
y ≥ 2x + 3
Rectangle
EFGH
was translated 4 units to the left and 6 units up. Which rule
describes the translation that was applied to rectangle EFGH to create rectangle
E'F'G'H?
(x,y) → (X-4.7+6)
(x,y) → (X-6.7+4)
(x,y) → (X+4.7-6)
(x,y) → (-44,64)
Answer:
(x, y) -- [X-4, Y+6]
Which equation below would be parallel to the line y - 2x = 8?*
O y = 2x + 5
O y = -2x + 8
O y = 10x - 3
O y = 6x + 2
11. Dave is building a doghouse that is a scale model of his shed in the farm yard, One of
the windows on the shed is 117 cm wide and 130 cm high. On the doghouse the window
is 9 cm wide,
a) What is the scale factor Dave is using to build the doghouse?
a.
2 mar
b) How high is the window in the scale model?
Answer:
a) 1/13 (or 13 depending on the factor is being applied to the dog house or applied to the shed. If its being applied to the shed like 117 * scale factor it is 1/13)
b) 10
Step-by-step explanation:
The scale factor is 13 and the height of the dog house is 10 cm.
What is scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object.
Given that, Dave is building a doghouse that is a scale model of his shed in the farmyard, One of the windows on the shed is 117 cm wide and 130 cm high. On the doghouse the window is 9 cm wide,
a) Since, the scale factor = ratio of original scale to scale of the model.
Therefore,
Scale factor = 117 / 9 = 13
b) Since, the scale factor is 13 and the original scale of the window high is 130 cm.
Therefore, height of the doghouse = 130 / 13 = 10 cm
Hence, the scale factor is 13 and height of the dog house is 10 cm.
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An electrician bent a section of copper wire into a partial circle as shown. The dimensions are
given in feet (ft).
2.5 f
880
2.5
ft
What is the length of the section of wire to the nearest hundredth of a foot?
Answer:
3.84 feets
Step-by-step explanation:
Given that:
θ = 88°
Radius, r = 2.5
The length of section of the wire, L ; Length of an arc
L = θ / 360° * 2πr
L = 88/360 * 2*π*2.5
L = (88/360) * 15.707963
L = 3.8397
Length of section of wire = 3.84 feets
PLEASE HELP!!1!!1!!11!!1!! I WILL MARK BRAINLIEST!!!!!!!!!111!111!!1!!11!
Answer:
s
Step-by-step explanation:
Answer:
fourth option) 5/8 lb
Determine the value of x in the triangle shown.
Question 2 options:
180°
45°
135°
90°
Answer:
135
Step-by-step explanation:
Hello There!
The angle that has a measure of 45° and x are supplementary angles meaning that the sum of the two angles is 180
so x can be found by subtracting the given angle (45 in this case) from 180
180 - 45 = 135
so x = 135
Answer:
135
Step-by-step explanation:
When there's a completely straight line the angle is 180 and when u have a angle already there you subtract 180 from the angle in this case 180-45=135
One of the objectives for this lesson is to find the length of a curve using the z score.
Answer:
The answer is "True".
Step-by-step explanation:
The z-score value shows how often standard deviations were away from the earth. If it is 0, it is on average. The positive Z sign indicates that perhaps the raw mark is greater than the average. While z-score is equivalent to +1, for example, it is a standard deviation of 1 above average. This can be used for implementing series and also for comparing the trend of mortality among various individuals or between various periods and by using the z score we find the curve length, that's why it is correct.
xf(3)+3f(x)=x+6 f(6)=?
4/5 x 7 need help asap
Answer:
4/5=0.8×7=5.6
5.6 is the answer
Hey there!
4/5 × 7
= 4×7/5
= 28/5
= 5.6
Hope it helps ya!
The lengths of time (in years) it took a random sample of 32 former smokers to quit smoking permanently are listed.
11.8 14.4 10.8 10.4 16.2 20.5 12.6 10.4 19.5 14.2 12.8 17.6 15.9 21.2 18.4 22.9 7.9 11.4 9.5 17.2 14.5 21.7 16.8 12.9 8.9 16.3 21.3 13.6 17.4 13.7 7.8 19.8
Assume the population standard deviation is 6.6 years. At α=0.09, is there enough evidence to reject the claim that the mean time it takes smokers to quit smoking permanently is 14 years? Complete parts (a) through (e).
(a) Identify the claim and state the null hypothesis and alternative hypothesis.
(b) Identify the standardized test statistic. Use technology.
(c) Find the P-value. Use technology.
(d) Decide whether to reject or fail to reject the null hypothesis and
(e) interpret the decision in the context of the original claim at the 10 % level of significance.
a. The null hypothesis is H₀: μ = 14 and alternative hypothesis is Ha: μ ≠ 14
b. The t-test for the data is 1.11
c. The p-value for the t-test is 0.28
d. We accept the null hypothesis since the p-value is greater than the significance value.
e. The decision to fail to reject the null hypothesis means that we do not have enough evidence to support the claim
What is the null and alternative hypothesis?(a) The claim is that the mean time it takes smokers to quit smoking permanently is 14 years.
Null hypothesis (H₀): The mean time it takes smokers to quit smoking permanently is 14 years.
H₀: μ = 14
Alternative hypothesis (Ha): The mean time it takes smokers to quit smoking permanently is not 14 years.
Ha: μ ≠ 14
(b) To identify the standardized test statistic, we can use the formula:
t = (x - μ) / (s / √n)
where:
x is the sample mean,
μ is the population mean,
s is the population standard deviation,
n is the sample size.
Given:
Sample mean (x) = 15.29375 (rounded to 5 decimal places)
Population mean (μ) = 14
Population standard deviation (s) = 6.6
Sample size (n) = 32
Using these values, we can calculate the standardized test statistic.
t = (15.29375 - 14) / (6.6 / √32)
t = 1.11
(c) To find the p-value, we need to use the t-distribution table or statistical software. Since using technology is mentioned in the question, we will use it to calculate the p-value.
The p-value for a two-tailed test is approximately 0.28.
(d) We compare the p-value to the significance level α = 0.09.
Since the p-value 0.28 is greater than the significance level (0.09), we fail to reject the null hypothesis.
(e) The decision to fail to reject the null hypothesis means that we do not have enough evidence to support the claim that the mean time it takes smokers to quit smoking permanently is different from 14 years at the 10% level of significance.
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Edward wrote a pattern starting at 0 and following the rule "add 2." . Juan wrote a pattern starting at 0 and following the rule "add 6." Which pair of patterns below represents that of Edward and Juan?
E: 1, 3, 5, 7, 9, ... J: 1, 7, 13, 19, 25, ...
E: 2, 4, 6, 8, 10, ... J: 6, 12, 18, 24, 30, ...
E: 0, 2, 4, 6, 8, ... J: 0, 6, 12, 18, 24, ...
E: 0, 2, 4, 8, 16, ... J: 0, 3, 9, 27, 81, ...
Answer:
the third option
Step-by-step explanation:
Answer:
3rd option
Step-by-step explanation:
they both started at 0 and added 2 and 6 respectively
A triangular prism has a base that is an isosceles triangle with sides 14 cm, 14cm , base 9 cm , and height 13 cm. The height of the prism is 32 cm. What is the surface area of this prism?
Answer:
Surface area of prism = 1301 cm²
Step-by-step explanation:
A triangular pyramid has 3 rectangular sides and 2 triangular sides.
Now, we are told that the triangular side is isosceles.
This means that two of the rectangular sides which share a side with the equal side of the triangle are equal as well as the 2 triangular sides.
Surface area of prism = 2(area of triangular face) + 2(area of rectangle sharing one side with the equal side of the triangle) + (area of rectangle sharing side with the unequal side of the triangle).
Area of triangle = ½ × base × height
Area of triangle = ½ × 9 × 13 = 58.5 cm²
Since height of prism is 32 cm, then;
area of rectangle sharing one side with the equal side of the triangle = 32 × 14 = 448 cm²
area of rectangle sharing side with the unequal side of the triangle = 32 × 9 = 288 cm²
Thus;
Surface area of prism = 2(58.5) + 2(448) + 288
Surface area of prism = 1301 cm²
A study was performed to test whether cars get better mileage on premium regular gas. Each of 10 cars was first filled with either regular or premium ss, coin toss, and the mileage for that tank was recorded. same cars using the other kind of gasoline. W significantly better mileage with premium gas. The mileage was recorded again for the e want to determine whether cars get reg- c(26, 29, 21, 22, 20, 22, 24, 2s, 25, 29) premC(19, 22, 24, 24, 2s, 25, 26, 26. 28, 32) a. What test should be used? b. What are the hypotheses? c. Based on the R outputs, what is your conclusion about hypotheses testing? data: prem and reg t-0.59702, df 9, p-value 0.2826 alternative hypothesis: true difference in means is greater thano 95 percent confidence interval: -1.656341 Inf sample estimates: mean of the differences 0.8
we do not have enough evidence to conclude that cars get better mileage on premium gasoline. Thus, we can conclude that there is no significant difference between the mileages of cars using premium and regular gasoline.
a. What test should be used?
The test that should be used is the Two-sample t-test because we are working with two independent groups.
b. What are the hypotheses?
The null hypothesis is that there is no difference between the mileage of cars using premium and regular gasoline, while the alternative hypothesis is that there is a difference between the two mileages.
Mathematically, this can be stated as follows: Null hypothesis: µ1 = µ2Alternative hypothesis: µ1 > µ2Where µ1 is the population mean for premium gasoline and µ2 is the population mean for regular gasoline.
c. Based on the R outputs, what is your conclusion about hypotheses testing?
From the R outputs, we can see that the p-value is 0.2826. Since this value is greater than the level of significance (α) of 0.05, we fail to reject the null hypothesis. Therefore, we do not have enough evidence to conclude that cars get better mileage on premium gasoline. Thus, we can conclude that there is no significant difference between the mileages of cars using premium and regular gasoline.
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a. The test that should be used is a two-sample t-test.
b. The null hypothesis is "The population mean mileage of cars using regular and premium gasoline are equal."
The alternative hypothesis is "The population mean mileage of cars using premium gasoline is more than the population mean mileage of cars using regular gasoline."
c. We do not have enough evidence to support the claim that cars get better mileage on premium regular gas.
a. To find what test should be used.
The test that should be used is a two-sample t-test.
b. To find the hypotheses.
The null hypothesis is "The population mean mileage of cars using regular and premium gasoline are equal."
The alternative hypothesis is "The population mean mileage of cars using premium gasoline is more than the population mean mileage of cars using regular gasoline."
c. Based on the R outputs, to find the conclusion about hypotheses testing.
The sample mean of the differences in mileage for cars filled with premium and regular gasoline is 0.8. The calculated t-value is -0.59702.
The calculated p-value is 0.2826.The p-value is higher than the significance level of 0.05.
Therefore, we fail to reject the null hypothesis.
We can't conclude that the population mean mileage of cars using premium gasoline is more than the population mean mileage of cars using regular gasoline.
Hence, we do not have enough evidence to support the claim that cars get better mileage on premium regular gas.
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NO LINKS!! Please help me out this is causing me stresss PLSS I posted this so many times and no answer plsss be kind and help me :’) Write the slope-intercept inequality for the graph below. If necessary, use <=
fors or >= for >
Answer:
Consider this option:
1. the equation of given line is y=-x-3 (it is easy to find it using points (0;-3)&(-3;0)).
2. according to the equation of line: y≥-x-3
i am a factor of 40 when you pair me with 15, my lcm of 15, i am not one
The number you are is 2.
Let's break down the information provided:
You are a factor of 40 when paired with 15.
Your least common multiple (LCM) with 15 is not equal to 1.
To find the number that satisfies these conditions, let's examine the factors of 40. The factors of 40 are 1, 2, 4, 5, 8, 10, 20, and 40. Now, we need to find a number from this list that is a factor of 40 when paired with 15.
To find the LCM of 15 and each factor of 40, we can compare their multiples:
For 15 and 1: LCM = 15
For 15 and 2: LCM = 30
For 15 and 4: LCM = 60
For 15 and 5: LCM = 15 (already the smaller number)
For 15 and 8: LCM = 120
For 15 and 10: LCM = 30 (already the smaller number)
For 15 and 20: LCM = 60 (already the smaller number)
For 15 and 40: LCM = 120 (already the smaller number)
From the list, we can see that the LCM of 15 with 5, 10, 20, and 40 is equal to 15. However, the problem states that the LCM of 15 with the number is not equal to 1. Thus, the number that satisfies both conditions is 2, as the LCM of 15 and 2 is 30, and it is not equal to 1. Therefore, the number you are is 2.
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help needed on no 8 pls
Answer:
I’m sorry, but it’s a black screen.
Step-by-step explanation:
how many meters are their in centimeter
Answer:
You mean how many centimerters are in a meter?
In that case 100.
Step-by-step explanation:
LAN tosses a bone up In the air for his dog, Spot. The height, h, in feet, that Spot is above the ground at the time t seconds after she jumps for the bone can be represented by the function h(t) = -16t^2 + 20t. What is Spots average rate of ascent, in feet per second, from the time she jumps into the air to the Time she catches the bone at t = 1/2 second?
Answer:
The rate of change is 12ft/s
Step-by-step explanation:
Given
[tex]h(t) = -16t^2 + 20t[/tex]
Required
Rate of change from when she jumps till 1/2s
The time she jumps is represented as: t = 0
So, calculate h(0)
[tex]h(t) = -16t^2 + 20t[/tex]
[tex]h(0) = -16 * 0^2 + 20 * 0 = 0[/tex]
At t = 1/2
[tex]h(t) = -16t^2 + 20t[/tex]
[tex]h(1/2) = -16 * 1/2^2 + 20 * 1/2 = 6[/tex]
Rate of change is calculated as:
[tex]Rate = \frac{f(b) - f(a)}{b - a}[/tex]
In this case:
[tex]Rate = \frac{h(b) - h(a)}{b - a}[/tex]
Where
[tex](a,b) = (0,1/2)[/tex]
So, we have:
[tex]Rate = \frac{h(b) - h(a)}{b - a}[/tex]
[tex]Rate = \frac{h(1/2) - h(0)}{1/2 - 0}[/tex]
[tex]Rate = \frac{6 - 0}{1/2 - 0}[/tex]
[tex]Rate = \frac{6}{1/2}[/tex]
[tex]Rate =12[/tex]
The rate of change is 12ft/s